When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have hierarchical relations. Previous works assume rigid consistency over the given hierarchies and do not adapt well to real-world data that show deviation from this assumption. Moreover, recent state-of-art neural probabilistic methods also impose hierarchical relations on point predictions and samples of the predictive distribution. This does not account for full forecast distributions being consistent with the hierarchy and leading to poorly calibrated forecasts. We close both these gaps and propose PROFHiT, a probabilistic hierarchical forecasting model that jointly models forecast distributions over the entire hierarchy. PROFHiT (1) uses a flexible probabilistic Bayesian approach and (2) introduces soft distributional consistency regularization that enables end-to-end learning of the entire forecast distribution leveraging information from the underlying hierarchy. This enables calibrated forecasts as well as adaptation to real-life data with varied hierarchical consistency. PROFHiT provides 41-88% better performance in accuracy and significantly better calibration over a wide range of dataset consistency. Furthermore, PROFHiT adapts to missing data and can provide reliable forecasts even if up to 10% of input time-series data is missing, whereas other methods' performance severely degrades by over 70%.